Is there a way to "colorize" a line drawing?

You can use the decodearray={rmin rmax gmin gmax bmin bmax} option to \includegraphics (the default colour coding is decodearray={0 1 0 1 0 1}).

\documentclass{article}
\usepackage{graphicx}
\begin{document}
\noindent
\includegraphics[decodearray={0 1 0 1 0 1},width=\textwidth]{ingmar.png}\\
\includegraphics[decodearray={1 1 0 1 0 1},width=\textwidth]{ingmar.png}\\
\includegraphics[decodearray={0 1 1 1 0 1},width=\textwidth]{ingmar.png}\\
\includegraphics[decodearray={0 1 0 1 1 1},width=\textwidth]{ingmar.png}
\end{document}

TikZ offers lots of possibilities of "filters" (not what kids these days know as filters, please) to apply over an image by using PDF transparency layers. Section 23.3 (Blend Modes) of the TikZ manual explains this feature with the possible "blend modes": normal, multiply, screen, overlay, darken, lighten, color dodge, color burn, hard light, soft light, difference, exclusion, hue, saturation, color and luminosity. Taking the example from this post, you can mix different blend modes to get interesting effects:

\documentclass{article}
\usepackage{tikz}
\begin{document}

\includegraphics[width=10cm]{hBg1w.png}

\newcommand\colorize[2]{
\begin{tikzpicture}
  \begin{scope}[blend group=#1]
    \begin{scope}[blend group=#2]
      \node[inner sep=0pt] (logo) {\includegraphics[width=10cm]{hBg1w}};
      \fill[white] (logo.south west) rectangle (logo.north east);
    \end{scope}
    \fill[red] (logo.south west) rectangle (logo.north east);
  \end{scope}
  \node (logo.south) [below=.5cm,font=\Large] {#1/#2};
\end{tikzpicture}

}

\colorize{screen}{overlay}
\colorize{overlay}{saturation}

%\colorize{screen}{normal}
%\colorize{screen}{multiply}
%\colorize{screen}{screen}
%\colorize{screen}{overlay}
%\colorize{screen}{darken}
%\colorize{screen}{lighten}
%\colorize{screen}{color dodge}
%\colorize{screen}{color burn}
%\colorize{screen}{hard light}
%\colorize{screen}{soft light}
%\colorize{screen}{difference}
%\colorize{screen}{exclusion}
%\colorize{screen}{hue}
%\colorize{screen}{saturation}
%\colorize{screen}{color}
%\colorize{screen}{luminosity}
\end{document}